
theorem Th73:
  for a being non empty Ordinal, b being Ordinal, n being non zero Nat
  st b in omega -exponent last CantorNF a
  holds CantorNF(a +^ (n*^exp(omega, b))) = CantorNF a ^ <% n*^exp(omega,b) %>
proof
  let a be non empty Ordinal, b be Ordinal, n be non zero Nat;
  assume A1: b in omega -exponent last CantorNF a;
  set A = CantorNF a, B = <% n*^exp(omega,b) %>;
  A2: CantorNF a ^ <% n*^exp(omega,b) %> is Cantor-normal-form by A1, Th37;
  Sum^(A^B) = Sum^ A +^ (n*^exp(omega, b)) by ORDINAL5:54
    .= a +^ (n*^exp(omega, b));
  hence thesis by A2;
end;
